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Statistics For The Behavioral Sciences 9th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions

A population consists of the following N = 5 scores: 0, 6, 4, 3, and 12.a. Compute m and σ for the population.b. Find the z-score for each score in the population.c. Transform the original population into a new population of N = 5 scores with a mean of µ = 100 and a standard deviation of σ = 20?
A sample consists of the following n = 6 scores: 2, 7, 4, 6, 4, and 7. a. Compute the mean and standard deviation for the sample. b. Find the z-score for each score in the sample. c. Transform the original sample into a new sample with a mean of M = 50 and s = 10?
A distribution has a standard deviation of σ = 6. Describe the location of each of the following z-scores in terms of position relative to the mean. For example, z = +1.00 is a location that is 6 points above the mean.a. z = + 2.00b. z = + 0.50c. z = -2.00d. z = -0.50
For a population with µ = 50 and σ = 8,a. Find the z-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.)b. Find the score (X value) that corresponds to
For a population with µ = 40 and σ = 7, find the z-score for each of the following X values. (You probably will need to use a formula and a calculator to find these values.)
For a population with a mean of ( = 100 and a standard deviation of ( = 12,a. Find the z-score for each of the following X values.b. Find the score (X value) that corresponds to each of the following z-scores.
A population has a mean of µ = 40 and a standard deviation of σ = 8.a. For this population, find the z-score for each of the following X values.b. For the same population, find the score (X value) that corresponds to each of the following z-scores.
A sample has a mean of M = 40 and a standard deviation of s = 6. Find the z-score for each of the following X values from this sample.
A sample has a mean of M = 80 and a standard deviation of s = 10. For this sample, find the X value corresponding to each of the following z-scores.
A local hardware store has a "Savings Wheel" at the checkout. Customers get to spin the wheel and, when the wheel stops, a pointer indicates how much they will save. The wheel can stop in any one of 50 sections. Of the sections, 10 produce 0% off, 20 sections are for 10% off, 10 sections for 20%, 5
Find the z-score location of a vertical line that separates a normal distribution as described in each of the following. a. 20% in the tail on the left b. 40% in the tail on the right c. 75% in the body on the left d. 99% in the body on the right
Find the z-score boundaries that separate a normal distribution as described in each of the following. a. The middle 20% from the 80% in the tails. b. The middle 50% from the 50% in the tails. c. The middle 95% from the 5% in the tails. d. The middle 99% from the 1% in the tails.
For a normal distribution with a mean of μ = 80 and a standard deviation of σ = 20, find the proportion of the population corresponding to each of the following scores.a. Scores greater than 85.b. Scores less than 100.c. Scores between 70 and 90?
A normal distribution has a mean of μ = 50 and a standard deviation of σ = 12. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail.a. X = 53b. X = 44c. X = 68d. X = 38
IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ = 15. Find the proportion of the population in each of the following IQ categories.a. Genius or near genius: IQ greater than 140b. Very superior intelligence: IQ between 120 and
The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT,a. What proportion have SAT scores greater than 700?b. What proportion have SAT scores greater than 550?c. What is the
The distribution of SAT scores is normal with μ = 500 and σ = 100.a. What SAT score, X value, separates the top 15% of the distribution from the rest?b. What SAT score, X value, separates the top 10% of the distribution from the rest?c. What SAT score, X value, separates the top 2% of the
A recent newspaper article reported the results of a survey of well-educated suburban parents. The responses to one question indicated that by age 2, children were watching an average of μ = 60 minutes of television each day. Assuming that the distribution of television-watching times is normal
Information from the Department of Motor Vehicles indicates that the average age of licensed drivers is μ = 45.7 years with a standard deviation of σ = 12.5 years. Assuming that the distribution of drivers' ages is approximately normal,a. What proportion of licensed drivers are older than 50
A consumer survey indicates that the average household spends μ = $185 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation of σ = $25. Based on this distribution,a. What proportion of the population spends more than $200 per week on
A psychology class consists of 14 males and 36 females. If the professor selects names from the class list using random sampling, a. What is the probability that the first student selected will be a female? b. If a random sample of n = 3 students is selected and the first two are both females, what
Over the past 10 years, the local school district has measured physical fitness for all high school freshmen. During that time, the average score on a treadmill endurance task has been μ = 19.8 minutes with a standard deviation of σ = 7.2 minutes. Assuming that the distribution is approximately
Rochester, New York, averages μ = 21.9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of σ = 6.5 inches. This year, a local jewelry store is advertising a refund of 50% off of all purchases made in December, if
A multiple-choice test has 48 questions, each with four response choices. If a student is simply guessing at the answers, a. What is the probability of guessing correctly for any question? b. On average, how many questions would a student get correct for the entire test? c. What is the probability
A true/false test has 40 questions. If a students is simply guessing at the answers, a. What is the probability of guessing correctly for any one question? b. On average, how many questions would the student get correct for the entire test? c. What is the probability that the student would get more
A roulette wheel has alternating red and black numbered slots into one of which the ball finally stops to determine the winner. If a gambler always bets on black to win, what is the probability of winning at least 24 times in a series of 36 spins? (Note that at least 24 wins means 24 or more.)
One test for ESP involves using Zener cards. Each card shows one of five different symbols (square, circle, star, cross, wavy lines), and the person being tested has to predict the shape on each card before it is selected. Find each of the probabilities requested for a person who has no ESP and is
A trick coin has been weighted so that heads occurs with a probability of p = 2/3, and p(tails) = 1/3. If you toss this coin 72 times, a. How many heads would you expect to get on average? b. What is the probability of getting more than 50 heads? c. What is the probability of getting exactly 50
For a balanced coin: a. What is the probability of getting more than 30 heads in 50 tosses? b. What is the probability of getting more than 60 heads in 100 tosses? c. Parts a and b both asked for the probability of getting more than 60% heads in a series of coin tosses (30/50 = 60/100 = 60%). Why
A national health organization predicts that 20% of American adults will get the flu this season. If a sample of 100 adults is selected from the population, a. What is the probability that at least 25 of the people will be diagnosed with the flu? (Be careful: "at least 25" means "25 or more.") b.
What are the two requirements that must be satisfied for a random sample? Discuss.
What is sampling with replacement, and why is it used?
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the tail. a. z = 2.00 b. z = 0.60 c. z = - 1.30 d. z = - 0.30
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body. a. z = 2.20 b. z = 1.60 c. z = - 1.50 d. z = - 0.70
Find each of the following probabilities for a normal distribution. a. p(z > 0.25) b. p(z > - 0.75) c. p(z < 1.20) d. p(z < - 1.20)
What proportion of a normal distribution is located between each of the following z-score boundaries? a. z = - 0.50 and z = + 0.50 b. z = - 0.90 and z = + 0.90 c. z = - 1.50 and z = + 1.50
Find each of the following probabilities for a normal distribution. a. p(-0.25 < z < 0.25) b. p(-2.00 < z < 2.00) c. p(-0.30 < z < 1.00) d. p(-1.25 < z < 0.25)
Briefly define each of the following: a. Distribution of sample means b. Expected value of M c. Standard error of M
For a population with a mean of μ = 80 and a standard deviation of σ = 12, find the z-score corresponding to each of the following samples.a. M = 83 for a sample of n = 4 scoresb. M = 83 for a sample of n = 16 scoresc. M = 83 for a sample of n = 36 scores
A sample of n = 4 scores has a mean of M = 75. Find the z-score for this sample:a. If it was obtained from a population with μ = 80 and σ = 10.b. If it was obtained from a population with μ = 80 and σ = 20.c. If it was obtained from a population with μ = 80 and σ = 40?
A population forms a normal distribution with a mean of μ = 80 and a standard deviation of σ = 15. For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size.a. M
A random sample is obtained from a normal population with a mean of μ = 30 and a standard deviation of σ = 8. The sample mean is M = 33.a. Is this a fairly typical sample mean or an extreme value for a sample of n = 4 scores?b. Is this a fairly typical sample mean or an extreme value for a sample
The population of IQ scores forms a normal distribution with a mean of μ = 100 and a standard deviation ofσ = 15. What is the probability of obtaining a sample mean greater than M = 97,a. for a random sample of n = 9 people?b. for a random sample of n = 25 people?
The scores on a standardized mathematics test for 8th-grade children in New York State form a normal distribution with a mean of μ = 70 and a standard deviation of σ = 10.a. What proportion of the students in the state have scores less than X = 75?b. If samples of n = 4 are selected from the
A population of scores forms a normal distribution with a mean of μ = 40 and a standard deviation of σ = 12.a. What is the probability of randomly selecting a score less than X = 34?b. What is the probability of selecting a sample of n = 9 scores with a mean less than M = 34?c. What is the
A population of scores forms a normal distribution with a mean of μ = 80 and a standard deviation of σ = 10.a. What proportion of the scores have values between 75 and 85?b. For samples of n = 4, what proportion of the samples will have means between 75 and 85?c. For samples of n = 16, what
At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of μ = 9 pounds with a standard deviation of σ = 6. The
The machinery at a food-packing plant is able to put exactly 12 ounces of juice in every bottle. However, some items such as apples come in variable sizes so it is almost impossible to get exactly 3 pounds of apples in a bag labeled "3 lbs." Therefore, the machinery is set to put an average of μ =
Describe the distribution of sample means (shape, expected value, and standard error) for samples of n = 36 selected from a population with a mean of μ = 100 and a standard deviation of σ = 12?
The average age for licensed drivers in the county is μ = 40.3 years with a standard deviation of σ = 13.2 years.a. A researcher obtained a random sample of n = 16 parking tickets and computed an average age of M = 38.9 years for the drivers. Compute the z-score for the sample mean and find the
People are selected to serve on juries by randomly picking names from the list of registered voters.The average age for registered voters in the county is μ = 44.3 years with a standard deviation of σ = 12.4.A statistician computes the average age for a group of σ = 12 people currently serving
Welsh, Davis, Burke, and Williams (2002) conducted a study to evaluate the effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance. Experienced athletes were given either a carbohydrate-electrolyte drink or a placebo while they were tested on a series of high-intensity
In the Preview section for this chapter, we discussed a research study demonstrating that 8-month-old infants appear to recognize which samples are likely to be obtained from a population and which are not. In the study, the infants watched as a sample of n = 5 ping pong balls was selected from a
A sample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8.a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M?b. If the sample has n = 16 scores, what is the expected value of M and the standard error of M?
The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?
A population has a standard deviation of σ = 30.a. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the population?b. On average, how much difference should exist for a sample of n = 25 scores?c. On average, how
For a population with a mean of μ = 70 and a standard deviation of σ = 20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of the following sample sizes?a. n = 4 scoresb. n = 16 scoresc. n = 25 scores
For a population with a standard deviation of σ = 20, how large a sample is necessary to have a standard error that is:a. Less than or equal to 5 points?b. Less than or equal to 2 points?c. Less than or equal to 1 point?
If the population standard deviation is σ = 8, how large a sample is necessary to have a standard error that is:a. Less than 4 points?b. Less than 2 points?c. Less than 1 point?
For a sample of n = 25 scores, what is the value of the population standard deviation (() necessary to produce each of the following a standard error values? a. (M = 10 points? b. (M = 5 points? c. (M = 2 points?
In the z-score formula as it is used in a hypothesis test,a. Explain what is measured by M - µ in the numerator.b. Explain what is measured by the standard error in the denominator?
Miller (2008) examined the energy drink consumption of college undergraduates and found that males use energy drinks significantly more often than females. To further investigate this phenomenon, suppose that a researcher selects a random sample of n = 36 male undergraduates and a sample of n = 25
A random sample is selected from a normal population with a mean of µ = 40 and a standard deviation of σ = 10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 42.a. How large a sample is necessary for this sample mean to be statistically
There is some evidence that REM sleep, associated with dreaming, may also play a role in learning and memory processing. For example, Smith and Lapp (1991) found increased REM activity for college students during exam periods. Suppose that REM activity for a sample of n = 16 students during the
There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). In a similar study, a researcher first obtained overall ratings of attractiveness for a woman with no tattoos shown in a color
A psychologist is investigating the hypothesis that children who grow up as the only child in the household develop different personality characteristics than those who grow up in larger families. A sample of n = 30 only children is obtained and each child is given a standardized personality test.
A researcher is testing the hypothesis that consuming a sports drink during exercise improves endurance. A sample of n = 50 male college students is obtained and each student is given a series of three endurance tasks and asked to consume 4 ounces of the drink during each break between tasks. The
Montarello and Martins (2005) found that fifth-grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that
Researchers have often noted increases in violent crimes when it is very hot. In fact, Reifman, Larrick, and Fein (1991) noted that this relationship even extends to baseball. That is, there is a much greater chance of a batter being hit by a pitch when the temperature increases. Consider the
A researcher plans to conduct an experiment testing the effect of caffeine on reaction time during a driving simulation task. A sample of n = 9 participants is selected and each person receives a standard dose of caffeine before being tested on the simulator. The caffeine is expected to lower
A sample of n = 40 is selected from a normal population with µ = 75 msec. and σ = 12, and a treatment is administered to the sample. The treatment is expected to increase scores by an average of 4 points.a. If the treatment effect is evaluated with a two-tailed hypothesis test using α = .05,
The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following: a. Increasing the difference between the sample mean and the original population mean. b.
Briefly explain how increasing sample size influences each of the following. Assume that all other factors are held constant. a. The size of the z-score in a hypothesis test. b. The size of Cohen's d. c. The power of a hypothesis test. Discuss.
Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant. a. Increasing the alpha level from .01 to .05. b. Changing from a one-tailed test to a two-tailed test?
A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systolic scores average µ = 160 with a standard deviation of σ = 20, and the scores form a normal-shaped distribution. The
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of µ = 80 and a standard deviation of σ = 20. The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with α = .05.a.
In words, define the alpha level and the critical region for a hypothesis test?
If the alpha level is changed from α = .05 to α = .01, a. What happens to the boundaries for the critical region? b. What happens to the probability of a Type I error?
Although there is a popular belief that herbal remedies such as ginkgo biloba and ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, & Nyberg, 2004). In a typical study, a researcher obtains
Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents (McGee, Williams, Howden- Chapman, Martin, & Kawachi, 2006). In a representative study, a sample of n = 100 adolescents with a history of group participation is
A local college requires an English composition course for all freshmen. This year they are evaluating a new online version of the course. A random sample of n = 16 freshmen is selected and the students are placed in the online course. At the end of the semester, all freshmen take the same English
A random sample is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.a. If the sample consists of n = 16 scores, is the sample mean sufficient to
A random sample of n = 36 scores is selected from a normal population with a mean of µ = 60. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 52.a. If the population standard deviation is σ = 18, is the sample mean sufficient to conclude that
Find each of the requested values for a population with a mean of µ = 40 and a standard deviation of σ = 8.a. What is the z-score corresponding to X = 52?b. What is the X value corresponding to z = - 0.50?c. If all of the scores in the population are transformed into z-scores, what will be the
A survey of female high school seniors shows that the average amount of time spent on clothes, hair, and makeup each morning before school is µ = 35 minutes. Assume that the distribution of preparation times is approximately normal with a standard deviation of σ = 14 minutes, and find each of the
Brunt, Rhee, and Zhong (2008) surveyed 557 undergraduate college students to examine their weight status, health behaviors, and diet. Using body mass index (BMI), they classified the students into four categories: underweight, healthy weight, overweight, and obese. They also measured dietary
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Discuss.
A random sample of n = 16 individuals is selected from a population with μ = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 76 with SS = 960. a. How much difference is there between the mean for the treated sample and the
The spotlight effect refers to overestimating the extent to which others notice your appearance or behavior, especially when you commit a social faux pas. Effectively, you feel as if you are suddenly standing in a spotlight with everyone looking. In one demonstration of this phenomenon, Gilovich,
Many animals, including humans, tend to avoid direct eye contact and even patterns that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off predators. Scaife (1976) reports a study examining how eye-spot patterns affect the behavior of
Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was µ = 15.1. A sample of n = 16 of today’s children produces a mean score of M = 23.3 with
The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample of n = 30 books and records the publication date for each. The sample produces an average age of M = 23.8 years with a variance of
For several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenomenon is called the Flynn effect after the researcher who first reported it (Flynn, 1984, 1999), and it means that psychologists must
In a classic study of infant attachment, Harlow (1959) placed infant monkeys in cages with two artificial surrogate mothers. One "mother" was made from bare wire mesh and contained a baby bottle from which the infants could feed. The other mother was made from soft terry cloth and did not provide
Belsky, Weinraub, Owen, and Kelly (2001) reported on the effects of preschool childcare on the development of young children. One result suggests that children who spend more time away from their mothers are more likely to show behavioral problems in kindergarten. Using a standardized scale, the
Other research examining the effects of preschool childcare has found that children who spent time in day care, especially high-quality day care, perform better on math and language tests than children who stay home with their mothers (Broberg, Wessels, Lamb, & Hwang, 1997). Typical results,
A random sample of n = 25 scores is obtained from a population with a mean of μ = 45. A treatment is administered to the individuals in the sample and, after treatment, the sample mean is M = 48. a. Assuming that the sample standard deviation is s = 6 compute r2 and the estimated Cohen's d to
A sample of n = 25 scores has a mean of M = 83 and a standard deviation of s = 15. a. Explain what is measured by the sample standard deviation. b. Compute the estimated standard error for the sample mean and explain what is measured by the standard error?
A random sample is obtained from a population with a mean of μ = 70. A treatment is administered to the individuals in the sample and, after treatment, the sample mean is M = 78 with a standard deviation of s = 20. a. Assuming that the sample consists of n = 25 scores, compute r2 and the estimated
An example of the vertical-horizontal illusion is shown in the figure below. Although the two lines are exactly the same length, the vertical line appears to be much longer. To examine the strength of this illusion, a researcher prepared an example in which both lines were exactly 10 inches long.

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